Critical level statistics at the Anderson transition in four-dimensional disordered systems

TL;DR

This study numerically investigates the critical level statistics at the Anderson transition in four-dimensional disordered systems, revealing deviations from random matrix theory and approaching Poisson statistics, with specific critical parameters identified.

Contribution

It provides the first detailed numerical analysis of level statistics at the Anderson transition in four dimensions, including critical disorder, correlation length exponent, and spectral compressibility.

Findings

Critical disorder W_c = 34.5 ± 0.5

Correlation length exponent ν = 1.1 ± 0.2

Critical spectral compressibility k_c ≈ 0.5

Abstract

The level spacing distribution is numerically calculated at the disorder-induced metal--insulator transition for dimensionality d=4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from the result of the random matrix theory compared to those of d=3 and to become closer to the Poisson limit of uncorrelated spectra. Using the finite size scaling analysis for the probability distribution Q_n(E) of having n levels in a given energy interval E we find the critical disorder W_c = 34.5 \pm 0.5, the correlation length exponent \nu = 1.1 \pm 0.2 and the critical spectral compressibility k_c \approx 0.5.